MCG 3345 FLUID MECHANICS II

Final Examination
Duration: 3 hrs.
16 April 1998
Professor S. Tavoularis
Open Book and Notes. Calculators Permitted.

1. The periscope of a submarine is mounted on a vertical, cylindrical tube, with a diameter of 120 mm and a height of 4 m. The submarine is moving horizontally with a constant speed of 10 km/hr.

a) Determine the total force and the total moment on the tube, when the tube is i) fully submerged, ii) fully exposed to the air, and iii) partly submerged; plot the force and moment vs. the submersion depth. (Marks: 25)

b) For the cases i) and ii) only above, determine the frequency of vortex shedding from the tube. (10)

Assume the salt water specific gravity to be 1.03 and its kinematic viscosity to be 1.25×10-6 m2/s. Explain and justify any other assumptions that you make.


2. Racing cars often use airfoils over their rear wheels to produce downthrust (i.e. downward lift) for better control. One design utilizes a NACA 23015 airfoil, with a chord of 300 mm and a length of 2.00 m, inclined at an angle of 12. Determine the downthrust produced by the airfoil, the total drag force on the airfoil and the engine power required by the airfoil, if the car is moving at 300 km/hr. (20)


3. A farmer needs to pump water from a well 40 m deep, at a flow rate of 0.02 m3/s. A number of surplus electric motors are available, all operating at a rotational speed of 900 rpm.

a) Can you use a single pump for this application? If so, what type would you recommend? If not, select the minimum number of identical pumps required, their types and the kind of connection (i.e. in parallel, in series or in any other combination); then, determine the flow rate and the head for each pump. (20)

b) Assuming that the suction pipes are large enough for the frictional losses and the kinetic energy in the pipes to be negligible, would you recommend to position the pump(s) on the ground level? If not, how deeply in the well would you put each pump and why? (10)


4. A Venturi tube is used to measure the mass flow rate of air through a pipe having a diameter of 45 mm. The throat diameter of the Venturi tube is 15 mm. For a particular test, the absolute static pressure at the inlet to the Venturi tube is 130 kPa, while that at the throat is 100 kPa. The temperature at the inlet is 17 C.

a) Assuming isentropic flow, determine the air densities at the inlet and at the throat and the temperature at the throat. (10)

b) Assuming isentropic flow, determine the air mass flow rate through the tube and the Mach number at the inlet (Hint: use the continuity and the energy equations for one-dimensional compressible flow). (15)

c) For the sake of exposing an erroneous procedure, assume frictionless, incompressible flow and determine the air mass flow rate, using Bernoulli's equation. Discuss the validity of this approach and determine the percent error that it would introduce. (5)

Total Marks (including a 15% bonus): 115%